加权Banach空间中随机指数系完备的若干结论

A Note on Random Exponential Approximation in the Weighted Banach Space

在允许随机序列上密度无限且减弱权函数是凸函数的条件下,采用新的方法得到C_α中随机指数函数系完备性的充分必要条件,其中C_α是定义在R上的复连续函数构成的加权Banach空间,且要求函数在一致范数下当t→∞时以f(t)exp(-α(t))趋于零.

Under the hypothesis of infinity upper density of random sequence is allowed and change a weaker condition of the power funtion a（t） instead of being convex. A new approach to obtain necessary and sufficient condition for the completeness of random exponential system in Ca is found, where C is the weighted Banach space of complex continuous functions f defined on the real axis R with f（t） exp（-a（t）） vanishing at infinity, in the uniform norm.